Interior-point algorithm for linear programming based on a new descent direction

Abstract

We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t)=t 7/4 . Furthermore, we show that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.